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A234787
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Cubes (with at least two digits) that become squares when their rightmost digit is removed.
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1
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1000, 64000, 729000, 4096000, 15625000, 46656000, 117649000, 262144000, 531441000, 1000000000, 1771561000, 2985984000, 4826809000, 7529536000, 11390625000, 16777216000, 24137569000, 34012224000, 47045881000, 64000000000
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OFFSET
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1,1
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COMMENTS
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With the help of the Nagell-Lutz theorem it is easy to prove that there are no other solutions than those of the form 1000*n^6.
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LINKS
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FORMULA
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a(n) = 1000*n^6.
G.f.: 1000*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
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PROG
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(PARI) lista(nn) = {for (n=1, nn, if (((cb = n^3) > 10) && issquare(cb\10), print1(cb, ", ")); ); } \\ Michel Marcus, Jan 10 2014
(PARI) Vec(1000*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Dec 15 2019
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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